A parametric study of buoyancy-driven flow of two-immiscible fluids in a differentially heated inclined channel

• The interfacial instability patterns.
• Significant change of vortical structures with temperature gradient between the walls.
• The critical Bond number is identified.
• Significant change of flow dynamics with increase in Marangoni number.

The buoyancy-driven interpenetration of two immiscible fluids in a differentially heated inclined channel is investigated by solving the Navier–Stokes, the continuity and the energy equations along with Cahn–Hillard equation to track the interface. After conducting a grid convergence test, a parametric study is conducted to investigate the effects of Reynolds number, Bond number, Marangoni number, density ratio, viscosity ratio and temperature difference between the walls (ΔT)(ΔT) on flow dynamics and interfacial instability between two immiscible fluids. We found that increasing Reynolds number, Bond number, ΔTΔT, density ratio and decreasing viscosity ratio destabilizes the flow dynamics by increasing the intensity of vortical structures and ‘mixing’ of the fluids. The flow dynamics of vortical structures are altered by the imposed temperature gradient between the walls in comparison with isothermal system. We found a critical Bo below which the surface tension force dominates the gravitational force for the set of parameter values considered, which in turn give rise to stationary stable interface.